Common wisdom holds it that a moving average approach is more successful than buy-and-hold. There is quantitative evidence for that across different asset classes (see e.g. this book, or this paper from the same author Mebane Faber).

My question takes a different turn: I am trying to generalize these empirical findings to a general class of stochastic processes.

My question:
What properties must a stochastic process have for moving average trading to outperform naive buy-and-hold. At the moment I am only talking about simple moving average strategies like when the process crosses the average from above/below sell/buy. There could also be simplifying assumptions like no trading costs etc.

The plan behind this is to find general properties which are empirically testable on their own. In a way I want to find the building blocks for moving average strategies to work.

+1: This is a good trace to follow - thank you!
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vonjdFeb 9 '11 at 15:46

Do I understand correct, you would like to prove such fact in the strict way? Then could you please clarify some points? The strategy will be either buy at a random moment (for buy and hold) or to buy (sell) only if you cross the MA from below (above). (i) Which MA are you talking about? (ii) How long do you expect to wait after buying (selling) to sell (buy)? I mean that you should define the class of strategies more precisely.
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IlyaFeb 21 '11 at 15:47